6.4 SAT Math - Formulas

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There aren't many formulas you need to have memorized on the SAT test, and most of them we'll encounter under geometry. There are two, however, that sometimes come up in algebra questions:

Distance Formula

This is NOT the one you are more likely working with in math class! If you immediately panicked or thought, "oh, of course!" that's not the one we're talking about. You don't need it, and we won't be talking about that stuff until Geometry anyway. Nope, we're talking the really basic science class one:

Knowing this formula will make certain word problems easier on the SAT exam. Example:
11. It takes Cami 1.5 hours to bike to work at rate of 10 mph. Assuming the same route and no stops, how long will it take her to bike home at twice that rate?
This can be solved other ways, but if you remember d = rt you'll be able to solve it in a much simpler way. We'll need one equation for her way to work, and one for her way home. So our first equation will be d1 = 10•1.5. What's her rate for the second equation? Twice the rate of earlier, so 20 mph. Our second equation will look like this: d2 = 20•t with t being how long it will take her to get home. What do we know about her two distances? They're both the same, right? Which means d1 = d2. That means we can simply set the two equations equal to each other and solve for t:

Starting Score Above 600:

Population/Interest Formula

You might also run into a question that tests population growth or interest earned. That formula is:

Where I is the interest earned, F is the final amount, P is the principal or starting amount, r is the rate in decimal, and t is time in years. Which one you use depends on whether you just want interest earned, or whether you want the total new amount in the account. Here's how you might see it:

19. On January 1, 1994, Mario invested money in an account that bore an average interest rate of 4.5% per year. He made no other deposits. At the end of 2008, he had $225,025 in the account. What was his initial investment to the nearest dollar?

Since the question gives us information relating to the final amount, we'll use the second equation, F = P(1 + r)t substituting in the information we know.

225000 = P(1 + .045)15

Why .045? 4.5% written as a decimal is .045. Why 15 instead of 14? Because he invested the money on January 1, 1994 and the final amount was calculated at the end of 2008 – which means he had the full year of 1994 and the full year of 2008, giving us 15 years worth of accrued interest instead of 14.